A parallelism \(\parallel\) of a projective space is an equivalence relation on the set of lines such that the Euclidean parallel postulate holds. An equivalence class of lines is then a set of mutually disjoint lines that cover the point set, normally called a ``line spread'' or more simply a ``spread'' when the context is clear. Parallelisms are of intrinsic interest for a variety of reasons of which one is the connection to translation planes. But, more fundamentally, it appears that geometers are interested in partitions of geometric objects, in general. In this article, a general survey of essentially all known results on parallelisms and partial parallelisms in projective spaces, both finite and infinite, is provided. In addition, a list of open questions is compiled. The material is exceptionally well organized and thoroughly treated. An extensive bibliography of some 55 references is given.